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ZeroMQ (also spelled ØMQ, 0MQ or ZMQ) is a high-performance asynchronous messaging library, aimed at use in distributed or concurrent applications. It provides a message queue, but unlike message-oriented middleware, a ZeroMQ system can run without a dedicated message broker.

The Guide

Libzmq - the low level library

Libzmq (https://github.com/zeromq/libzmq) is the low-level library behind most of the different language bindings.
Libzmq expose C-API and implemented in C++.
You will rarely use libzmq directly, however if you want to contribute to the project or learn the internals of zeromq, that is the place to start.